XI Maths, Example 1.1, Sets, Relations and Functions,

Example 1.1 Find the number of subsets of A if A = {x : x = 4n + 1, 2 ≤ n ≤ 5, n ∈ N}. Solution: Given that n ∈ N and 2 ≤ n ≤ 5 ⟹ n = 2, 3, 4, 5 x = 4n + 1 x = 4(2)+1; x = 4(3)+1; x = 4(4)+1; x = 4(5)+1 = 8 + 1 ; = 12 + 1 ; = 16 + 1; = 20 + 1 = 9 ; = 13 ; = 17 ; = 21 ⟹ A = {9, 13, 17, 21} Hence n(A) = 4 ⟹ n[P(A)] = 2x2x2x2 = 16